Vibration analysis of a plate with an arbitrarily orientated surface crack

TJ Mechanical engineering and machinery

Ismail, Rainah ; Philip Cartmell, Matthew

University:University of Glasgow

Department:School of Engineering

关键词: vibration analysis, cracked plate, an arbitrarily orientated crack;   

Others  :  http://theses.gla.ac.uk/4002/1/2012IsmailPhd.pdf

来源: University of Glasgow

【 摘 要 】

This research presents a vibration analysis for a thin isotropic plate containing an arbitrarily orientated surface crack. The work has been motivated by the well known applicability of various vibrational techniques for structural damage detection in which the detection and localisation of damage to thin plate structures at the earliest stage of development can optimise subsystem performance and assure a safer life, and is intended to be an enhancement to previous work on cracked plates for which the orientation of the crack angle was not included. The novelty of this research activity has been in the assimilation of a significantly enhanced crack model within the analytical model of the plate, in modal space, and taking the form of a specialised Duffing equation. The governing equation of motion of the plate model with enhanced crack modelling is proposed to represent the vibrational response of the plate and is based on classical plate theory into which a developed crack model has been assimilated. The formulation of the angled crack is based on a simplified line-spring model, and the cracked plate is subjected to transverse harmonic excitation with arbitrarily chosen boundary conditions. In addition, the nonlinear behaviour of the cracked plate model is investigated analytically from the amplitude-frequency equation by use of the multiple scales perturbation method. For both cracked square and rectangular plate models, the influence of the boundary conditions, the crack orientation angle, crack length, and location of the point load is demonstrated. It is found that the vibration characteristics and nonlinear characteristics of the cracked plate structure can be greatly affected by the orientation of the crack in the plate. The dynamics and stability of the cracked plate model are also examined numerically using dynamical systems tools for representing the behaviour of this system for a range of parameters. Finally the validity of the developed model is shown through comparison of the results with experimental work and finite element analysis in order to corroborate the effect of crack length and crack orientation angle on the modal parameters, as predicted by the analysis. The results show excellent predictive agreement and it can be seen that the new analytical model could constitute a useful tool for subsequent investigation into the development of damage detection methodologies for generalised plate structures.